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The Oberwolfach problem, posed by Ringel in 1967, asks for a decomposition of K2n+1 into edge-disjoint copies of a given 2-factor. We show that this can be achieved for all large n. We actually prove a significantly more general result, which allows for decompositions into more general types of factors. In particular, this also resolves the Hamilton-Waterloo problem for large n. [ABSTRACT FROM AUTHOR]

We prove that if T1, ..., Tn is a sequence of bounded degree trees such that Ti has i vertices, then Kn has a decomposition into T1, ..., Tn. This shows that the tree packing conjecture of Gyárfás and Lehel from 1976 holds for all bounded degree trees (in fact, we can allow the first o.n/ trees to have arbitrary degrees). Similarly, we show that Ringel's conjecture from 1963 holds for all bounded degree trees. We deduce these results from a more general theorem, which yields decompositions of dense quasi-random graphs into suitable families of bounded degree graphs. Our proofs involve Szemerédi's regularity lemma, results on Hamilton decompositions of robust expanders, random walks, iterative absorption as well as a recent blow-up lemma for approximate decompositions. [ABSTRACT FROM AUTHOR]